Discrete Math — Permutations in Practice
In the former article, we saw various ideas behind multiple formulas and theorems in discrete math concerning permutations. As stated in the former article, a permutation is an arrangement of some elements in which order matters. In other words, a Permutation is an ordered combination of elements. In this article, we will put these theorems to practice so we can understand them better — and know how we can use them for real-life questions.
Multiplication Theorem in Practice
Imagine that you have gotten a new phone and now you must choose a password for it. The password has the following rules:
- It consists of 4 symbols
- The first two symbols are chosen between the first 10 letters in the English alphabet.
- The last two symbols are digits between 0 and 4.
How many different passwords can you make for your new phone? In this question, we can clearly use the theorem of multiplication. We can say that we have 4 tasks — each one is choosing a symbol. The first two tasks, T_1 and T_2 have 10 possible options each. The last two tasks, T_3 and T_4, have 4 possible options each. So, we need to do T_1T_2T_3T_4, which is equal to doing 10*10*5*5 = 2500. In the end, we have 2500 possible passwords. We can illustrate it:
